Answer:
48 feet
Explanation:
So first find the amount of fence they would need in terms of x, which would be (x - 2) + (3x - 1) + (5x + 8) + (3x - 1) + (x - 2). Then, you know these add up to 106 so you get the equation:
![x-2+3x-1+5x+8+3x-1+x-2 = 106](https://img.qammunity.org/2022/formulas/mathematics/high-school/nwjbjanb0esvqntls0ogs1qcyge97pmpar.png)
Now, you just have to solve.
First, combine like terms
![13x + 2 = 106](https://img.qammunity.org/2022/formulas/mathematics/high-school/ysm6akhqfg4is5qvr19vyoc4dugkbsbi4y.png)
Then, subtract 2 from both sides
![13x = 104](https://img.qammunity.org/2022/formulas/mathematics/high-school/eyovsmryae7rwmbodl34h0lqi8tfvugrrx.png)
Next, divide both sides by 13.
![x = 8](https://img.qammunity.org/2022/formulas/mathematics/college/7o7boqadzzw5kr7nyfulfplvsdyu5lhigb.png)
The last step is to find the length of 5x + 8 by substituting x = 8 in
![5*8+8=40+8=48](https://img.qammunity.org/2022/formulas/mathematics/high-school/4ib1wd4qullzr1frtcy1s3yj1x6c0twg2l.png)